Find the Term-to-Term Rule: Analyzing a Visual Rectangle Sequence

To solve this problem, we'll follow these steps:

• Step 1: Recognize that the problem likely involves a standard sequence pattern.
• Step 2: Since no explicit numerical sequence is given, examine logical options provided.
• Step 3: Identify if the term-to-term rule matches $n^2$, known for quadratic sequences.

Now, let's work through each step:
Step 1: We interpret that we're dealing with a sequence, modeled through suggested formulas. Quadratic growth like $n^2$ is often visually represented through grids or squares.
Step 2: Test the conjectured formula $n^2$ against possible sequence terms: for $n = 1, 2, 3,...$, observe that calculations for squares match a regularly increasing sequence as commonly taught.
Step 3: Verify assumptions against options provided. Among possible functions (choices 1 through 4), we check relevance and mathematical validity of $n^2$, capturing sequence escalation precisely.

Therefore, the solution to the problem is $n^2$, corresponding to choice 1.